Near wellbore modeling method and apparatus

ABSTRACT

Method of generating a hybrid grid allowing modelling of a heterogeneous formation crossed by one or more pipes such as, for example, an underground formation where one or more wells have been drilled, in order to form a representative model for example of fluid flows in this medium in accordance with a defined numerical pattern.  
     The method essentially comprises associating a first structured grid for gridding of the heterogeneous medium respecting the discontinuities thereof with a second structured, radial type grid for gridding of a zone around each pipe or well, which allows to better respect particular constraints linked with flows in this zone, and transition non-structured grids that are interposed between the first grid and each second well grid. Various grids are combined, each with its own formation, representation and exploration methods, structured grids which are advantageous in that they facilitate control and comprehension of the reservoir images formed and more flexible non-structured grids for gridding of complex zones.  
     Applications: hydrocarbon reservoir simulators for example.

FIELD OF THE INVENTION

[0001] The present invention relates to a method of generating a hybridgrid allowing modelling of a heterogeneous formation crossed by one ormore pipes.

[0002] The method is more particularly applied to formation of a gridsuited to an underground reservoir crossed by one or more wells, inorder to model displacements of fluids such as hydrocarbons

BACKGROUND OF THE INVENTION

[0003] Grid generation is a crucial element for the new generation ofreservoir simulators. Grids allow to describe the geometry of thegeologic structure studied by means of a representation in discreteelements wherein simulation is performed according to a suitablenumerical pattern. Better comprehension of physical phenomena requires3D simulation of the multiphase flows in increasingly complex geologicstructures, in the vicinity of several types of singularities such asstratifications, faults, pinchouts, channels and complex wells. All thiscomplexity has to be taken into account first by the grid which has toreproduce as accurately as possible the geologic information in itsheterogeneous nature.

[0004] Grid modelling has made great advances during the past few yearsin other fields such as aeronautics, combustion in engines, structuremechanics, etc. However, the gridding techniques used in the otherfields cannot be applied as they are to the petroleum sphere because theprofessional constraints are not the same. For example, in reservoirsimulation, the numerical patterns are constructed from control volumesin order to better respect the mass conservation in the case oftransport equations of hyperbolic nature. The grid must be a<<block-centered>> type grid, i.e. the nodes must be inside each layerand the boundaries of each block must follow the interface between thelayers. Now, if this constraint was not taken into account, the nodeswould naturally be placed along the faults and along the stratificationboundaries. The consequence of this would be that these interfaces wouldpass through the control volume used. The saturation, constant in thecontrol volume, could not respect then the discontinuity and the resultswould not be accurate. It is therefore necessary to develop newtechniques that are better suited to the petroleum sphere requirements.

[0005] Cartesian grids, which are commonly used in current commercialsimulators, are unsuited for solving these new problems posed by thedevelopment of petroleum reservoirs. Cartesian grids, based onparallelepipedic elements, do not allow representation of such complexgeometries.

[0006] There is a well-known method of generating structured 3Dhexahedral grids of CPG (Corner-Point-Geometry) type which respects thegeometry of the bodies. It is described in patent FR-2,747,490 (U.S.Pat. No. 5,844,564) filed by the applicant and also in the followingpublication:

[0007] Bennis Ch. Et al. <<One More Step in Gocad Stratigraphic GridGeneration>>: Taking into Account Faults and Pinchouts; SPE 35526,Stavanger, 1996.

[0008] This grid type is more flexible than Cartesian grids because itconsists of any hexahedral elements that can be degenerated. It strictlyrespects the horizons, the faults and it allows to represent certainunconformities such as pinchouts because its construction is based onthese elements. However, this type of grid does not allow to solve allthe geometric complexities such as, for example, circular radial gridsaround complex wells. It is possible to form separately the grid of thereservoir and the grids around the wells but it is difficult torepresent several objects in the same CPG type reservoir grid because ofconnection problems linked with the structured nature of the grid.

[0009] Another approach is also known where 3D grids only based ontetrahedral Delaunay elements, with a circular radial refinement aroundthe wells, are automatically generated. The advantage of such anapproach is that it is entirely automatic and does practically notrequire the user's attention. However, this method has drawbacks whichmake the results obtained difficult to use:

[0010] there are on average five times as many grid cells as in a CPGtype grid for the same structure, which is very disadvantageous forsimulation calculations,

[0011] unlike the structured grids which are easy to visualize, toexplore from the inside and to locally modify interactively, it is verydifficult and sometimes impossible to properly control the tetrahedralgrids because of their size and especially because of theirnon-structured nature. This poses problems for validating the grid froma geometric point of view as well as for understanding and validatingthe result of a simulation on this type of grid.

[0012] Other approaches are also well-known, which allow to generategrids, notably grids based on control volumes generated from atriangulation (Voronoï and CVFE), associated with techniques ofaggregation of the triangles (or tetrahedrons) into quadrangles allowingthe number of grid cells to be reduced. Although promising results wereobtained with these new grids, precise representation of the geologiccomplexity of reservoirs and wells remains a subject for research anddevelopment. In fact, these grids are rather 2.5D (i.e. verticallyprojected) and their 3D extension appears to be very difficult. Despitetheir hybrid aspect, they remain entirely unstructured and wouldtherefore be very difficult to manage and to handle in real 3D.Furthermore, taking account of real 3D faults and deviated wells wouldgreatly increase this difficulty.

SUMMARY OF THE INVENTION

[0013] The method according to the invention allows to generate a hybridgrid suited to a heterogeneous formation crossed by at least one pipe ofknown geometry (such as an underground reservoir crossed by one or morewells), in order to form a model representative of fluid flows in thisformation in accordance with a defined numerical pattern, the structureof the formation being known a priori from available data acquired bymeans of in-situ measurements, analyses and/or interpretations offormation images (seismic images for example, in the case of areservoir).

[0014] The method is characterized in that it comprises associating afirst structured grid for gridding of the formation while respecting thediscontinuities thereof with second structured, radial type grids forgridding of the zones around the wells, these second grids allowing torespect constraints linked with the flows in the wells, andnon-structured transition grids between the first grid associated withthe formation and the second grids associated with the wells.

[0015] Gridding of the heterogeneous medium is obtained for example byimporting each second structured grid into a cavity formed in the firststructured grid, the size of this cavity being sufficient to allowformation of a non-structured transition grid between the firststructured grid associated with the formation and the second structuredgrid associated with each well.

[0016] The non-structured transition grid based on any polyhedrons orcanonical polyhedrons such as pentahedrons, tetrahedrons, pyramids,etc., can be formed by respecting constraints linked with the numericalpattern.

[0017] The non-structured transition grids are advantageously modelledwith the structured well grids by applying a formalism known in the art,referred to as <<generalized map>> formalism, the grid of the formationbeing structured matrically, globally or in faulted blocks.

[0018] The global hybrid grid is thus obtained by combination of severalgrid types: a structured reservoir grid, a radial grid around each well,also structured, and non-structured transition grids which connect theprevious two grid types. Each one of these grids has its own formation,representation and exploration methods. The structured aspect is thusdegraded only at the points where this is strictly necessary. This<<object>> approach affords both the advantage of structured grids forcontrol and comprehension of the reservoir and the flexibility ofnon-structured grids in complex zones. Complexity is introduced onlywhere it is strictly necessary. The independence of these gridding modestherefore allows separate extraction, management and representation ofthe well grids and of the interstitial grids included in the reservoirgrid.

[0019] Using a reservoir simulator of a well-known type, such as ATHOS™or SCORE™ for example, for a reservoir provided with a hybrid gridobtained by means of the method, allows production simulations to beperformed.

BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Other features and advantages of the method according to theinvention will be clear from reading the description hereafter of nonlimitative examples, with reference to the accompanying drawingswherein:

[0021]FIG. 1 shows a diagrammatic example of a hybrid grid of areservoir crossed by two wells, consisting of a first structured gridfor the reservoir, a second structured grid for the zones around thewells and transition grids between the two grid types,

[0022]FIG. 2 shows an example of a structured grid of a faultedreservoir,

[0023]FIG. 3 shows an example of a radial grid around a vertical well,

[0024]FIG. 4 shows an example of grid of a horizontal well,

[0025]FIG. 5 shows, in 2.5D, an example of a gridded reservoir wherecavities are provided for gridded wells, before the stage of creation ofnon-structured interstitial grids intended to connect them together,

[0026]FIG. 6 shows five wells provided each with a radial grid, includedin a gridded reservoir, by means of non-structured transition gridsbased on any polyhedral grid cells,

[0027]FIG. 7 shows separately the structured reservoir grid with thecavities provided therein in order to include the additional elements:gridded wells and interstitial grids,

[0028]FIGS. 8A, 8B, 8C, 8D show elementary well grids visualizedindividually according to different modes,

[0029]FIGS. 9A, 9B, 9C, 9D show various elementary transition grids,visualized individually according to different modes, also, allowingtheir integration into the reservoir grid,

[0030]FIG. 10 shows an example of a hybrid reservoir grid withtransition grids consisting for example of pentahedrons, between thereservoir grid and several well grids,

[0031]FIG. 11 shows a model for the matrical representation of astructured grid around a well,

[0032]FIG. 12 is a graphic representation of a connection betweenstrands, within the scope of the modelling technique referred to as<<generalized maps>> technique used for generating non-structured grids,

[0033]FIGS. 13A, 13B are graphic representations of connections by meansof simple arcs, and

[0034]FIGS. 14A, 14B are graphic representations of connections by meansof double or triple arcs respectively.

DETAILED DESCRIPTION

[0035] Modelling of the reservoir is obtained by combining elementarygrids of different types. Each elementary grid is considered to be afull object with its own data model, its own generation methods and itsown representation methods. Generation is carried out in stages withaddition/subtraction of grids.

[0036] 1) In order to represent the reservoir as a whole, an i, j, kstructured grid of a type known to specialists, referred to as CPG(Corner Point Geometry), as described in the aforementioned patentFR-2,747,490 is used for example. The reservoir can be faulted withdowncreep of a block in relation to the other. The major horizons andfaults are first modelled by continuous surfaces from data resultingfrom an interpretation of seismic images of the subsoil or from dataobtained during drilling (well markers). The geologic structure is thendivided into faulted blocks resting on these surfaces. These blocks areindividually gridded, then reassembled. Gridding of a block firstconsists in gridding the edge surfaces, then the inside is populated bytransfinite interpolation of the edge surface grids. Relaxationtechniques are then applied to the edge surfaces and to the inside so asto harmonize and to regulate the grid. The grid thus obtained strictlyrespects the horizons, the faults and it allows to represent certainunconformities such as pinchouts. It meets all the constraints ofgeologic nature.

[0037] 2) A well trajectory is drawn synthetically or imported. Astructured radial grid is then generated around each well in order totake account of the particular constraints linked with the flows in thevicinity of these wells.

[0038] In the example shown in FIG. 3, the structure grid around avertical well is of circular radial type. It is also a CPG type grid.Its generation first consists in sampling a disc at r, θ in thehorizontal plane. The 2D grid thus obtained is then projected verticallyupon the various layers of the reservoir grid. Here, the i, j, k of thematrical structure correspond to the samplings at r, θ and zrespectively (see FIG. 11).

[0039] The grid around a horizontal well (FIG. 4) is i, j, k structured,it is of the same type as that of the reservoir, except that a wellcannot be faulted. It is also obtained by projecting vertically upon thevarious layers of the reservoir grid a 2D grid belonging to a horizontalplane.

[0040] 3) This radial grid is then inserted around the or around eachwell in the global reservoir grid. A cavity is therefore first createdin the reservoir grid by deactivating all the grid cells in contact withwell grid cells (FIGS. 5, 6). The space freed between the reservoir gridand the well grid must be sufficient to allow convenient formation of atransition grid. It can represent for example about the equivalent oftwo grid cell layers.

[0041] 4) A non-structured transition grid is then generated in thiscavity (FIG. 7) in order to connect the structured radial grid aroundthe well to that of the reservoir best respecting the constraints linkedwith the numerical pattern. The user can deactivate the grid of a wellany time by reactivating the grid cells of the corresponding cavity inthe reservoir grid.

[0042] The transition grid can for example consist of polyhedrons withany number of sides or canonical polyhedrons (tetrahedrons,pentahedrons, pyramids, etc.) according to the numerical pattern used,without the overall hybrid approach proposed being affected.

[0043] Example of Modelling of a Hybrid Grid

[0044] The reservoir grid and each well grid are modelled, for eachfaulted block of the reservoir, by matrical structures of points orcells comprising each eight points. Because of the structured nature ofthe grids, the topological links between the various grid cells areimplicitly contained in the matrical structure.

[0045] Transition grids are more difficult to manage because of theirnon-structured nature and because they can contain polyhedral grid cellswhose number of sides varies from one cell to the other.

[0046] An advantageous solution for facilitating management of this newgrid type, allowing to browse it and to surf it efficiently, consists inusing the topological model referred to as <<generalized maps orG-maps>>. This model known to specialists is for example described by:

[0047] Edmond J.: <<A Combinatorial Representation for PolyhedralSurfaces>>, Notice Amer. Math. Soc., 7, 1960, or by:

[0048] Fortune S., 1992: Voronoi diagrams and Delaunay triangulations,pp.225-265 of D. Z. Du & F. K. Hwang (eds.), Computing in EuclideanGeometry, 2^(nd) edn. Lecture Notes Series on Computing, vol.4,Singapore, World Scientific.

[0049] Generalized maps are based on a formal algebraic approach that isbriefly reminded hereafter.

[0050] In 3D, the elements which constitute a generalized map are (D,α₀, α₁, α₂, α₃), where D is a finite set of elements called strands, andelements {α_(i)} are involution on D type functions, associating thestrands two by two at most, which are therefore conveniently referred toas links. FIGS. 11 to 14 show concrete geometric representationexamples. Link α₀ is in the form of a dotted segment (FIG. 11) and linksα₁, α₂ and α₃ in the form of arcs, respectively simple (FIG. 12), double(FIG. 13) and triple (FIG. 14).

[0051] According to another known approach, generalized maps areconsidered as graphs whose strands form the nodes and the links form thearcs: link α₀ between two strands can be used for representing the edgeof a side, links α₁ for connecting two edges of a side, links α₂ forlinking two sides of a cell together and links α₃ for sticking two cellstogether.

[0052] This model of generalized maps involves a small number of formalobjects and an operation which, by associating additional informationwith a topology, allows to locate the objects defined in space and toaccount for their appearance, which is referred to as plunge and, in thepresent case, plunge in a 3D space.

[0053] It affords the advantage of being independent of the dimension ofthe objects. All the objects can be represented with the same datastructure and handled with the same methods. This approach makes itpossible to handle objects created with heterogeneous topologicalmodels. It is therefore well-suited for implementing the methodaccording to the invention with its stage of creation of anon-structured grid linking two different structured grids together.

[0054] The generalized map concept for modelling the transition grid isapplied by creating a certain number of objects of different types whichrefer to one another. These objects materialize the topological networkand its various plunges in a 3D space. Concretely, in order to allowbrowsing the grid, a topological network is constructed parallel to thegeometric data commonly handled in a grid, the points, the edges, thesides and the cells. Furthermore, crossed links are established betweenthe topological network and geometric data.

[0055] Objects

[0056] The various objects handled within the scope of the applicationperformed here of the generalized map method are as follows:

[0057] 1) The Transition Grid object which contains all the topology,the geometry and the physical data. It consists of a GMap type objectwhich represents the topological network and of a Plunge type objectwhich materializes the plunge in the physical world according to ourapplication.

[0058] 2) The GMap Object

[0059] The topological model is entirely contained in a graph consistingof a list of Strands connected to one another. Any operation performedon the generalized map amounts to an operation on the Strands network.The GMap object type has methods allowing easy circulation in thetopological network representing the grid, i.e. to go from one Strand toanother.

[0060] 3) The Strand Object

[0061] Each Strand is defined by four references to other Strands(corresponding to links (α₀, α₁ and α₃) and by four other references tothe plunge in the 3D space, notably at a Point, an Edge, a Side and at aCell to which it is connected.

[0062] 4) The Plunge Object

[0063] It is defined by four lists

[0064] a list of Points (the grid points), it is the plunge of dimension0 of the GMap,

[0065] a list of Edges (plunge of dimension 1 of the GMap),

[0066] a list of Sides (plunge of dimension 2 of the GMap), and

[0067] a list of Cells (plunge of dimension 3 of the GMap).

[0068] The Plunge object also contains its own methods of creating andhandling the data it contains according to the use that is made thereof.Besides, the GMap is created from its Plunge.

[0069] 5) The Point Object

[0070] A Point is defined by its coordinates x, y, z and by a list ofattributes, notably scalar or real petrophysical values that areassociated therewith.

[0071] 6) The Edge Object

[0072] It is defined by a reference in the GMap to a Strand whichrepresents an end of the Edge. This gives a preferential access to thetopological network and simultaneously allows to go from the plunge tothe strands graph. For example, link α₀ of the Strand in question leadsto the Strand representing the other end of the Edge. It is furthermoredefined by a list of attributes, notably scalar or real petrophysicalvalues that are associated therewith.

[0073] 7) The Side Object

[0074] This type of object allows to handle directly the interfacesbetween the cells as well as the outer sides of the grid. A side isdefined by a reference in the GMap to a Strand which represents a vertexof the edge polygon of the Side. This also gives a preferential accessto the topological network. The Strands representing the other verticesof the polygon are accessible by iterative applications of the relationα₀∘α₁ by starting from the initial Strand and eventually coming back tothis same Strand. It is also defined by a list of attributes relative tothe Side (for example, scalar or vector petrophysical values).

[0075] 8) The Cell Object

[0076] The type of Cell object is defined by a list of references in theGMap to Strands, each one representing a half-Side of the Cell. Thisallows access to the topological network from the Cells. It is alsodefined by a site (coordinates of the center of mass of the Cell) and bya list of attributes specific to the Cell or to its site (scalar orvector petrophysical values for example).

[0077] Graphical Representation and Exploration

[0078] A graphical representation is a very efficient and even essentialmeans for controlling and validating the construction of a grid and thesimulation results. Concerning the construction, the geometry of thegrid generated is generally first visually controlled. If this is notsufficient, local or global quality criteria with which statistics areestablished can be calculated and visualized on the grid by means of acolour scale. Flow simulation consists in calculating the variationswith time of certain petrophysical parameters by taking account of thehypotheses that initially condition the flows. Simulation validationalso involves visualization of these parameters on the grid (preferablyby means of a colour scale). As the grids concerned are 3D grids, toolsallowing to explore the grid from the inside by visual browsing arerequired. Graphical representation and browsing in the grids, presentedhereafter, are a good illustration of the flexibility and the modularityof the hybrid approach proposed and of the efficiency and the adequacyof the data model selected.

[0079] The hybrid grid, considered as a set of independent entities: theelementary grids, is constantly visualized in a main window. The usercan select at any time an elementary grid and visualize it with itsspecific methods in a secondary window which contains only theelementary grid selected. Actions on the elementary grid haveautomatically repercussions on the entire hybrid grid visualized in themain window. An elementary grid can thus be visualized and explored as afull entity and it can be viewed in the global context. Thevisualization methods differ according to whether the elementary grid isstructured (reservoir grid and well grids) or not (transition grids).

[0080] Examples of Functionalities Specific to Structured Grids

[0081] In the case of a structured grid (reservoir and well),visualization is simple and conventional. It consists in two mainfunctionalities:

[0082] visualization of the external envelope of the grid with thepossibility of peeling it in the 3 directions i, j, k separately,

[0083] simultaneous or separate visualization of three matrical cellslices i=cste, j=cste and k=cste, with the possibility of moving them inthe block.

[0084] Examples of Functionalities Specific to Non-Structured Grids

[0085] In the case of non-structured transition grids, other, moreelaborate visualization modes are preferably used. Five functionalitiesare mainly used:

[0086] visualization of the external envelope with the possibility ofconcentric peeling, topologically speaking,

[0087] visualization of the cells crossed by a cutting plane orthogonalto an axis of coordinates x, y, z or any axis,

[0088] visualization of the trace of the cells on the cutting plane,

[0089] visualization of the grid sites when they are intially given and

[0090] visualization of the grid cells in full or scattered mode.

[0091] Of course, for the two grid types, it is possible to visualize aproperty or scalar value by means of a colour scale.

[0092] All these functionalities require easy and optimum viewing of thenon-structured grid. This is possible by using the formalism referred toas generalized map formalism.

[0093] FIGS. 7 to 10 clearly illustrate the potential afforded by thehybrid grid method proposed, i.e. harmonious integration of a structuredgrid following a topological model (well grid) into another structuredgrid (reservoir grid) following a different topological model, by meansof a non-structured transition grid. The independence of these modelstherefore allows extraction and separate representation of the wellgrids and of the interstitial grids included in the reservoir grid inorder to represent, handle and explore this type of data.

1. A method of generating a hybrid grid suited to a heterogeneousformation crossed by at least one pipe or well of known geometry, inorder to form a model representative of fluid flows in this medium inaccordance with a defined numerical pattern, the structure of theformation being known a priori from available data acquired throughin-situ measurements, analyses and/or interpretations of images of theformation, including associating a first structured grid for griddingthe formation by respecting the discontinuities thereof with secondstructured, radial type grids for gridding of the zones around thewells, these second grids allowing to respect constraints linked withflows in wells, characterized in that a non-structured transition gridformed by applying the process referred to as generalized map process,is inserted between the first structured grid associated with theformation and each second structured grid associated with a well.
 2. Amethod as claimed in claim 1 , characterized in that the secondstructured grid is imported in a cavity, the size of this cavity beingsufficient to allow formation of a non-structured transition gridbetween the first structured grid associated with the formation and thesecond structured grid associated with each well, the non-structuredtransition grid being formed by respecting constraints linked with saidnumerical pattern, the first structured grid being matricallystructured, globally or by faulted blocks.
 3. A method for simulating,in accordance with a defined numerical pattern, the evolution of aprocess such as fluid flows in a heterogeneous medium crossed by atleast one pipe or well of known geometry, the structure of the formationbeing known a priori from available data acquired through in-situmeasurements, analyses and/or interpretations of formation images,including forming a hybrid grid by associating a first structured gridfor gridding the formation by respecting the discontinuities thereof asecond, radial type structured grid for gridding a zone around eachwell, these second grids allowing to respect constraints linked withflows in the wells, characterized in that it includes inserting anon-structured transition grid formed by applying a process referred toas generalized map process, between the first structured grid associatedwith the formation and each second structured grid associated with thewells, and solving the numerical pattern in the hybrid grid formed forthe medium in order to simulate the process.